You said rich I presumed you were talking about millionaires/billionaires. Previous PM's were hardly in that category, they may of been well off but that's hardly the same.
As for Thatchers father, grocery stores back in the day were small affairs not great supermarkets of today, maggie had to help out in her youth and said it was very hard work. They lived in the flat above the shop, she bragged often about her humble past, hardly Paris Hilton eh?
John Majors father was a music hall performer, if you know anything about the UK, you would know that's far from a rich profession, John Major spent his youth unemployed and did odd jobs here and there like bus conductor (he too bragged in later years about this)
Tony Blair's father was adopted by a shipyard worker and his wife and worked as a tax inspector to get himself through uni, his mum was the daughter of a butcher, yet again Blair bragged of these humble roots. His father became a university lecturer but that's even less pay than a doctor over here. Both Tony Blair and John Major had crappy jobs at The Electricity board in their youth.
Gordon Brown was the son of a vicar, so no sipping champagne for him lol.
James Callaghan was the son of a CPO in the navy, worked in the tax office and then a union.
Harold Wilson, son of an industrial chemist and a school teacher.
Only our present PM was born with a silver spoon in his mouth, him and his wife come from very rich privileged backgrounds, as much as I despise him, I do believe he got to his position on merit.